Prior art discloses several branches of compression algorithms. Statistical methods of compression relied on reducing the size of frequent patterns in data. Compression was based on redundancy of the data and often involved the work of Shannon and others. There were practical limits to compressing data with redundancy.
Prior art compression is statistical. Compression is based on redundancy modeling. The present invention allows checksums to be used to determine whether a number in a sequence of numbers matches a given checksum and to make files smaller. Currently, files are limited by the amount of redundancy that can be removed. A checksum compressor would operate on how unique a number is by the uniqueness of the checksum—i.e., there is only one checksum number that can be associated with a given number.
Message digests were created to verify that data is the original data and that no changes occurred in transmission. They can be used to ensure that computer files have not been modified. There are two main message digests and signature hashes used today, Secure Hash Algorithm (“SHA”) and Message Digest Algorithm No. 5 (“MD5”). MD5 is one of the first message digest algorithms1 created and was developed by Rivest-Shamir-Adleman (“RSA”). As is known in the art, MD5 has a problem with collisions, and is not guaranteed to be as unique as SHA. 1Other message digest algorithms include MD2 (a message-digest hash function optimized for 8-bit machines), and MD4 (a message-digest hash function optimized for 32-bit machines).
SHA was developed by the U.S. government (N.S.A) to fingerprint computer data. The government developed SHA as a means of verifying digital information. SHA is a quest for generating a unique key or hash for a given set of data. One of the primary government interests is in tracking data and transmission of data. There are numerous open source implementations of the SHA algorithm in C and C++ code.
This is a note from the US government about SHA security, however, it should not be considered the assertion of the US government.                This document specifies a Secure Hash Algorithm, SHA-1, for computing a condensed representation of a message or a data file. When a message of any length<2^64 bits is input, the SHA-1 produces a 160-bit output called a message digest. The message digest can then, for example, be input to a signature algorithm which generates or verifies the signature for the message. Signing the message digest rather than the message often improves the efficiency of the process because the message digest is usually much smaller in size than the message. The same hash algorithm must be used by the verifier of a digital signature as was used by the creator of the digital signature. Any change to the message in transit will, with very high probability, result in a different message digest, and the signature will fail to verify.        The SHA-1 is called secure because it is computationally infeasible to find a message which corresponds to a given message digest, or to find two different messages which produce the same message digest. Any change to a message in transit will, with very high probability, result in a different message digest, and the signature will fail to verify.        
Both SHA and MD5 are known in the art, and further description is not provided herein.